Bindweed - must destroy, but how?

Got a new allotment and it has several mature fruit bushes (gooseberries and blackcurrants) plus a real bindweed problem. It is easy to rip it out as it has taken over and is actually growing higher than the fruit bushes. I thought it needed something to climb up. I have pulled most of it out and will keep going until I can't see any more.

I have heard that if you leave any of it behind it will come back next year. I keep spotting bits I missed and wonder does it grow again if there are some bits of stem hitting the ground?

Interesting thing there appear to be loads of bud on the stems that were covered by the bindweed that never came out. Is this a problem? I was wondering if these buds would impede any new buds forming next year. There were some gooseberries still on the bush, most gone over ripe but tried one and it is quite a nice tasting one so I'm happy for next year. There were also a few very large blackcurrants under all the weeds, grass and bindweed. They were as big as grapes. Biggest blackcurrants I've seen. Can you get big currants?

I also need to prune the bushes anything I need to know? I've got a lot to learn about allotments and growing stuff so please pass on your knowledge.

Good advice re Roundup. It's a bit cheaper if you just buy generic glyphosate. Bear in mind that the idea is to get the living leaves to suck up the herbicide into its nether regions, so the plant has to be growing.
Once you get rid of the bindweed you will be able to see to prune later in the year. You are basically pruning out all the dead, or misshapen wood and shortening the longer branches by a third. . In the case of goosberries prune out the middle of the bush so you can reach the fruits without being lacerated by thorns.
There's loads of useful articles on this site for the new allotment holder so have a good read of them as well.
Good luck